Correcting systematic errors in diffraction data with modern scaling algorithms

Abstract

X-ray diffraction enables the routine determination of the atomic structure of materials. Key to its success are data-processing algorithms that allow experimenters to determine the electron density of a sample from its diffraction pattern. Scaling, the estimation and correction of systematic errors in diffraction intensities, is an essential step in this process. These errors arise from sample heterogeneity, radiation damage, instrument limitations and other aspects of the experiment. New X-ray sources and sample-delivery methods, along with new experiments focused on changes in structure as a function of perturbations, have led to new demands on scaling algorithms. Classically, scaling algorithms use least-squares optimization to fit a model of common error sources to the observed diffraction intensities to force these intensities onto the same empirical scale. Recently, an alternative approach has been demonstrated which uses a Bayesian optimization method, variational inference, to simultaneously infer merged data along with corrections, or scale factors, for the systematic errors. Owing to its flexibility, this approach proves to be advantageous in certain scenarios. This perspective briefly reviews the history of scaling algorithms and contrasts them with variational inference. Finally, appropriate use cases are identified for the first such algorithm, Careless, guidance is offered on its use and some speculations are made about future variational scaling methods.

High-resolution double vision of the allosteric phosphatase PTP1B

“…Unlike most other PTP1B structures, the unusual crystal form of our new structure also accommodates two copies of the protein in distinct crystal-packing environments. The distinct patterns of crystal contacts experienced by these two chains within the same asymmetric unit (Table 2) allowed us to perform controlled comparisons of the conformational ensemble of PTP1B without the need to scale structure factors across data sets (Aldama et al, 2023) or normalize B factors across models (Ringe & Petsko, 1986;Carugo & Argos, 1997;Vihinen et al, 1994). Notably, the chain that was least impacted by crystal contacts exhibited noticeably higher disorder, with visually dispersed electron density, higher B factors (Table 2, Fig.…”

High-resolution double vision of the archetypal protein tyrosine phosphatase

“…Unlike most other PTP1B structures, our new structure’s unusual crystal form also accommodates two copies of the protein in distinct crystal packing environments. The distinct patterns of crystal contacts experienced by these two chains within the same asymmetric unit ( Table 2 ) allowed us to perform controlled comparisons of the conformational ensemble of PTP1B, without the need to scale structure factors across datasets (Aldama, Dalton, and Hekstra 2023) or normalize B-factors across models (Ringe and Petsko 1986; Carugo and Argos 1997; Vihinen, Torkkila, and Riikonen 1994). Notably, the chain that was least impacted by crystal contacts exhibited noticeably higher disorder, with visually dispersed electron density, higher B-factors ( Table 2, Fig.…”

Laue-DIALS: open-source software for polychromatic X-ray diffraction data

“…The integrated intensities obtained from Laue-DIALS still need to be corrected for variations in the wavelengths giving rise to each reflection (because incident flux, absorption, and scattering depend on wavelength), for the overlap of harmonics, and for other factors not specific to Laue diffraction, such as radiation damage, beam polarization, and variations in diffracting volume during rotation. 30 Here, we infer and apply the relevant correction factors (or scale factors) using the program Careless, which performs simultaneous inference of the scales of reflections and their merged structure factor amplitudes 13 . III.…”